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isSAGBI(SAGBIBasis) -- Check if the generators are a subalgebra basis



Checks whether the subalgebra generators of a SAGBIBasis $SB$ form a subalgebra basis. The result of the computation is stored in the sagbiStatus of $SB$. Subsequent calls of isSAGBI on $SB$ will look up the result of the sagbiStatus unless the option Recompute is set to true. If the option Compute is set to false, then isSAGBI attempts to find a previously cached result. If isSAGBI cannot determine a result without computation and the option Compute is set to false, then isSAGBI returns null.

If the subalgebra generators of $SB$ form a subalgebra basis, then the partial subalgebra basis is updated, unless ModifySAGBIBasis is set to false. If the option UseSubringGens is set to true, then the generators of the subring of $SB$ are used instead of the subalgebra generators of the subring.

i1 : R = QQ[x,y,z];
i2 : S = subring {x+y+z,x*y+x*z+y*z, x*y*z, (x-y)*(x-z)*(y-z)};
i3 : isSAGBI S

o3 = false
i4 : isSAGBI sagbi(S, Limit => 5)

o4 = false
i5 : S' = subring {x+y,x*y,x*y^2,x*y^7-y};
i6 : isSAGBI S'

o6 = false
i7 : isSAGBI sagbi(S', Limit => 5)

o7 = false
i8 : isSAGBI sagbi(S', Limit => 10)

o8 = true

The options Subduction strategies, SubductionMethod, PrintLevel, and RenewOptions are only used when performing a subalgebra bases computation.

See also

Ways to use this method: